# How do you normalize (- 3 i + 12j -k)?

Mar 14, 2018

$\frac{1}{\sqrt{154}} \left(- 3 \setminus \hat{i} + 12 \setminus \hat{j} - \setminus \hat{k}\right)$

#### Explanation:

You have to calculate the square root of the sum of squares (magnitude) of the vector:

$\sqrt{{\left(- 3\right)}^{2} + {\left(12\right)}^{2} + {\left(- 1\right)}^{2}} = \sqrt{9 + 144 + 1} = \sqrt{154}$

Now you simply divide the entire vector by this quantity to normalize:

$\frac{1}{\sqrt{154}} \left(- 3 \setminus \hat{i} + 12 \setminus \hat{j} - \setminus \hat{k}\right)$